The difference between the highest and the lowest observations in a data is its
range
Understanding the Range of Data
In the field of statistics and data analysis, when we look at a data set, we often want to understand how spread out the observations are. One simple way to measure this spread is by finding the difference between the highest and the lowest values present in the data.
This specific difference is known as the range. It gives us a quick idea of the overall variability within the data.
What is the Range?
The range of a data set is calculated by subtracting the lowest observation from the highest observation. Mathematically, it is represented as:
\(\text{Range} = \text{Highest Observation} - \text{Lowest Observation}\)
For example, if a data set consists of the numbers 10, 15, 20, 25, 30, the highest observation is 30 and the lowest observation is 10. The range would be \(30 - 10 = 20\).
Why Other Options are Incorrect for Measuring Data Spread (Highest vs Lowest)
- Frequency: Frequency tells us how many times a particular observation or value appears in the data set. It does not measure the difference between the highest and lowest values.
- Width: In the context of grouped data, width usually refers to the class width or the size of an interval. While related to how data is organized, it's not the simple difference between the absolute highest and lowest observations in the entire set.
- Mode: The mode is the observation that appears most frequently in the data set. It indicates the most common value, not the spread between the highest and lowest values.
Therefore, the term that specifically describes the difference between the highest and the lowest observations in a data set is the range.
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